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Cut a sphere by a plane in such a way that the volumes of the spherical segments have a given ratio.

Construct a 5×5×5 cube from thirteen 1×2×4 blocks, one 2×2×2 block, one 1×2×2, and three 1×1×3 blocks.

A fractal curve of infinite length which bounds an area twice that of the original square.

The slicing of a three-dimensional object by a plane (or more general slice).

The divergence of a vector field F, denoted div(F) or del ·F (the notation used in this work), is defined by a limit of the surface integral del ·F=lim_(V->0)(∮_SF·da)/V (1) ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

An a×b rectangle can be packed with 1×n strips iff n|a or n|b.

A ruled surface M is a normal developable of a curve y if M can be parameterized by x(u,v)=y(u)+vN^^(u), where N is the normal vector (Gray 1993, pp. 352-354; first edition ...

A loose term for a true statement which may be a postulate, theorem, etc.

Assemble six 1×2×2 blocks and three 1×1×1 blocks into a 3×3×3 cube.